Autoregressive surrogate modeling for dynamical systems
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2025-09-05
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Abstract
Numerical simulations are essential tools for predicting the behavior of real-world systems. They support the design of robust and cost-efficient civil structures and therefore contribute to public safety. In practical applications, one must often account for uncertainty in the simulator inputs (e.g. material properties, geometry, or loading conditions) since it translates into uncertainty in the model response (deflections or stresses). Understanding how the input uncertainty affects the system response is the objective of uncertainty quantification (UQ).
A standard approach in UQ is Monte Carlo simulation, which estimates output variability by evaluating many input scenarios. While conceptually simple, this method can be impractical when the computational cost of repeated simulations is high.
To address this, surrogate models are used as fast mathematical approximations of the full simulation, built from a limited number of simulator runs. However, constructing accurate surrogates from limited data is challenging, especially for dynamical systems, where the response evolves over time according to complex physical laws. For example, in a bridge exposed to variable traffic and wind loads, small uncertainties in material properties or loading history can lead to significantly different deflection patterns as time progresses. The behavior of such systems is therefore often difficult to emulate accurately using conventional surrogate modeling techniques.
A promising class of surrogates to model dynamical systems is the family of nonlinear autoregressive with exogenous inputs (NARX) models, which use past system states to predict future responses. This approach enforces the causality inherent in any dynamical system, thus improving long-term accuracy. Although effective in many settings, classical NARX models show limitations when applied to highly complex systems or when data is limited.
This thesis advances NARX-based surrogate modeling for complex dynamical systems through three main contributions. First, we develop the manifold-NARX (mNARX) model, which enhances the expressiveness of classical NARX by hierarchically incorporating prior knowledge and auxiliary system data. It constructs structured sequences of simpler intermediate models, improving forecast stability and accuracy in data-limited settings. This makes mNARX particularly useful in engineering applications where such additional information is available.
Second, we introduce functional-NARX (F-NARX), a formulation tailored to systems with long memory. Instead of using raw time lags, F-NARX works with temporal features and leverages the smoothness and continuity of the underlying physical process. This mitigates the curse of dimensionality, enhances generalization, and improves robustness to the time discretization of the data.
Third, we present an automated framework that builds on the structure of F-NARX to construct mNARX models directly from data. This replaces the previously manual and heuristic-driven model-building process with a systematic, data-driven approach. By recursively identifying causal patterns in the data and organizing the surrogate accordingly, the resulting workflow is less labor-intensive and more scalable, making mNARX modeling more accessible in practice.
The proposed methodologies are validated on a range of case studies, including analytical examples and complex engineering systems such as wind turbines and multi-story buildings. In all cases, the surrogate models demonstrate high accuracy, strong long-term predictive capabilities, and computational efficiency. This work therefore provides a practical foundation for surrogate modeling of dynamical systems and expands the possibilities for uncertainty quantification in many engineering applications.
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ETH Zurich
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Doctoral Examination - Public Part
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03962 - Sudret, Bruno / Sudret, Bruno
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101006689 - HIghly advanced Probabilistic design and Enhanced Reliability methods for high-value, cost-efficient offshore WIND (EC)